Finite Group Databasebeta

← C32×C4×D3×C9 #14518876

Subgroups — C32×C4×D3×C9 #14518876

Order 1944.

1244 conjugacy classes of subgroups; only the 550 normal subgroups are shown.

normal subgroups only

This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 550 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×C9C211yesmaximal, characteristic
2C33×C4×C9C211yesmaximal, characteristic, complemented
3C32×C9×Dic3C211yesmaximal, characteristic, complemented
4C33×C4×D3C311yesmaximal, characteristic
5C2×C32×C4×C9—31nomaximal
6C3×C4×D3×C9C3112yesmaximal, direct product factor
7C2×C33×C9C2211yescharacteristic
8C32×D3×C9C412yesdirect product factor
9C2×C33×D3C2×C311yescharacteristic
10C34×C4C2×C311yescharacteristic
11C33×Dic3C2×C311yescharacteristic
12C22×C32×C9—31no—
13C2×C3×D3×C9C2×C3112yes—
14C32×C4×C9—21no—
15C32×C4×C9—212no—
16C32×C4×C9—31no—
17C32×C4×C9D311yescharacteristic, direct product factor
18C32×C4×C9C2×C3112yescomplemented
19C3×C9×Dic3C2×C3112yescomplemented
20C33×C9C2×C411yescharacteristic, complemented, Sylow
21C2×C33×C4—31no—
22C32×C4×D3C919yesdirect product factor
23C32×C4×D3C3214yes—
24C2×C3×C4×C9—312no—
25C4×D3×C9C3219yesdirect product factor
26C2×C34C22×C311yescharacteristic
27C33×D3C3×C412yes—
28C2×C32×C9—21no—
29C2×C32×C9—212no—
30C2×C32×C9—32no—
31C2×C32×C9C2×D311yescharacteristic
32C2×C32×C9C22×C3112yes—
33C3×D3×C9C3×C4124yesdirect product factor
34C22×C33—31no—
35C2×C32×D3C2×C919yes—
36C2×C32×D3C2×C3214yes—
37C33×C4—29no—
38C33×C4—24no—
39C33×C4—31no—
40C33×C4C2×C919yescomplemented
41C33×C4C3×D311yescharacteristic
42C33×C4C2×C3214yes—
43C32×Dic3C2×C919yescomplemented
44C32×Dic3C2×C3214yes—
45C22×C3×C9—312no—
46C2×D3×C9C2×C3219yes—
47C3×C4×C9—212no—
48C3×C4×C9—236no—
49C3×C4×C9—312no—
50C3×C4×C9C3×D3112yesdirect product factor
51C3×C4×C9C2×C3219yescomplemented
52C9×Dic3C2×C3219yescomplemented
53C34C2×C3×C411yescharacteristic
54C32×C9—21no—
55C32×C9—212no—
56C32×C9C4×D311yescharacteristic, direct product factor
57C32×C9C2×C3×C4112yescomplemented
58C2×C32×C4—39no—
59C2×C32×C4—34no—
60C3×C4×D3C3×C9112yesdirect product factor
61C3×C4×D3C3311yescharacteristic
62C2×C4×C9—39no—
63C2×C33—29no—
64C2×C33—24no—
65C2×C33—32no—
66C2×C33C22×C919yes—
67C2×C33C2×C3×D311yescharacteristic
68C2×C33C22×C3214yes—
69C32×D3C4×C9118yesdirect product factor
70C32×D3C32×C418yes—
71C2×C3×C9—212no—
72C2×C3×C9—236no—
73C2×C3×C9—324no—
74C2×C3×C9C2×C3×D3112yes—
75C2×C3×C9C22×C3219yes—
76D3×C9C32×C4118yesdirect product factor
77C22×C32—39no—
78C22×C32—34no—
79C2×C3×D3C2×C3×C9112yes—
80C2×C3×D3C2×C3311yescharacteristic
81C32×C4—236no—
82C32×C4—212no—
83C32×C4—24no—
84C32×C4—39no—
85C32×C4—34no—
86C32×C4D3×C919yesdirect product factor
87C32×C4C2×C3×C9112yescomplemented
88C32×C4C32×D314yes—
89C32×C4C2×C3311yescharacteristic
90C3×Dic3C2×C3×C9112yescomplemented
91C3×Dic3C2×C3311yescharacteristic
92C22×C9—39no—
93C4×C9—29no—
94C4×C9—39no—
95C4×C9C32×D319yesdirect product factor
96C33—29no—
97C33—24no—
98C33C2×C4×C919yescomplemented
99C33C3×C4×D311yescharacteristic
100C33C2×C32×C414yes—
101C3×C9—212no—
102C3×C9—236no—
103C3×C9C3×C4×D3112yesdirect product factor
104C3×C9C2×C32×C419yescomplemented
105C2×C3×C4—312no—
106C2×C3×C4—31no—
107C4×D3C32×C911yescharacteristic, direct product factor
108C2×C32—236no—
109C2×C32—212no—
110C2×C32—24no—
111C2×C32—318no—
112C2×C32—38no—
113C2×C32C2×D3×C919yes—
114C2×C32C22×C3×C9112yes—
115C2×C32C2×C32×D314yes—
116C2×C32C22×C3311yescharacteristic
117C3×D3C3×C4×C9124yesdirect product factor
118C3×D3C33×C412yes—
119C2×C9—29no—
120C2×C9—318no—
121C2×C9C2×C32×D319yes—
122C22×C3—312no—
123C22×C3—31no—
124C2×D3C2×C32×C911yescharacteristic
125C3×C4—212no—
126C3×C4—21no—
127C3×C4—312no—
128C3×C4—31no—
129C3×C4C3×D3×C9112yesdirect product factor
130C3×C4C2×C32×C911yescharacteristic, complemented
131C3×C4C33×D311yescharacteristic
132Dic3C2×C32×C911yescharacteristic, complemented
133C32—24no—
134C32—236no—
135C32—212no—
136C32C4×D3×C919yesdirect product factor
137C32C2×C3×C4×C9112yescomplemented
138C32C32×C4×D314yes—
139C32C2×C33×C411yescharacteristic
140C9—29no—
141C9C32×C4×D319yesdirect product factor
142C2×C4—31noSylow
143C2×C3—212no—
144C2×C3—21no—
145C2×C3—32no—
146C2×C3—324no—
147C2×C3C2×C3×D3×C9112yes—
148C2×C3C22×C32×C911yescharacteristic
149C2×C3C2×C33×D311yescharacteristic
150D3C32×C4×C912yesdirect product factor
151C22—31no—
152C4—31no—
153C4C32×D3×C911yescharacteristic, direct product factor
154C3—212no—
155C3—21no—
156C3C3×C4×D3×C9112yesdirect product factor
157C3C2×C32×C4×C911yescharacteristic, complemented
158C3C33×C4×D311yescharacteristic
159C2—32no—
160C2C2×C32×D3×C911yescharacteristic
subgroupG/H
center, hypercenterC32×C4×C9D3
commutator, hypocenterC3C2×C32×C4×C9
FrattiniC2×C3C2×C33×D3
FittingC33×C4×C9C2
socleC2×C34C22×C3
prime radicalC2×C33×D3C2×C3
cosocleC2×C32C22×C33
LCSG ▷ C3
UCSC1 ◁ C32×C4×C9

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C33×C4×C9C2semidirect
3. C32×C9×Dic3C2semidirect
6. C3×C4×D3×C9C3direct (N × H)
8. C32×D3×C9C4direct (N × H)
17. C32×C4×C9D3direct (N × H)
18. C32×C4×C9C2×C3semidirect
19. C3×C9×Dic3C2×C3semidirect
20. C33×C9C2×C4semidirect
22. C32×C4×D3C9direct (N × H)
25. C4×D3×C9C32direct (N × H)
33. C3×D3×C9C3×C4direct (N × H)
40. C33×C4C2×C9semidirect
43. C32×Dic3C2×C9semidirect
50. C3×C4×C9C3×D3direct (N × H)
51. C3×C4×C9C2×C32semidirect
52. C9×Dic3C2×C32semidirect
56. C32×C9C4×D3direct (N × H)
57. C32×C9C2×C3×C4semidirect
60. C3×C4×D3C3×C9direct (N × H)
69. C32×D3C4×C9direct (N × H)
76. D3×C9C32×C4direct (N × H)
86. C32×C4D3×C9direct (N × H)
87. C32×C4C2×C3×C9semidirect
90. C3×Dic3C2×C3×C9semidirect
95. C4×C9C32×D3direct (N × H)
98. C33C2×C4×C9semidirect
103. C3×C9C3×C4×D3direct (N × H)
104. C3×C9C2×C32×C4semidirect
107. C4×D3C32×C9direct (N × H)
117. C3×D3C3×C4×C9direct (N × H)
129. C3×C4C3×D3×C9direct (N × H)
130. C3×C4C2×C32×C9semidirect
132. Dic3C2×C32×C9semidirect
136. C32C4×D3×C9direct (N × H)
137. C32C2×C3×C4×C9semidirect
141. C9C32×C4×D3direct (N × H)
150. D3C32×C4×C9direct (N × H)
153. C4C32×D3×C9direct (N × H)
156. C3C3×C4×D3×C9direct (N × H)
157. C3C2×C32×C4×C9semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C32×D3×C92
C33×C4×C92
C32×C9×Dic32
C33×C4×D33
C2×C32×C4×C93
C3×C4×D3×C93